Simplify the following expression: $r = \dfrac{8y^2 + 104y + 288}{y + 4} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ r =\dfrac{8(y^2 + 13y + 36)}{y + 4} $ Then we factor the remaining polynomial: $y^2 + {13}y + {36} $ ${4} + {9} = {13}$ ${4} \times {9} = {36}$ $ (y + {4}) (y + {9}) $ This gives us a factored expression: $\dfrac{8(y + {4}) (y + {9})}{y + 4}$ We can divide the numerator and denominator by $(y - 4)$ on condition that $y \neq -4$ Therefore $r = 8(y + 9); y \neq -4$